On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy

ABSTRACT Stress‐constrained reliability‐based topology optimization (RBTO) method has incurred considerable attention owing to its superiority of enhancing the structural safety. However, the traditional reliability methods encounter inaccurate issue for evaluating the failure probability of stress‐constrained structure. In this work, the failure mechanism of the stress‐constrained RBTO problem is analyzed for continuum structure, which reveals that the correlation between different stress constraints and utilization of aggregation function significantly impacts the accuracy. Then, a novel stress‐constrained system RBTO framework is suggested to enhance computational efficiency and accuracy for system reliability analysis. Furthermore, an accurate and efficient semi‐analytical method is suggested to approximate the performance functions through first‐order Taylor series expansion, in which the intricate implicit expressions are substituted by the straightforward analytic expressions. In addition, the fidelity transformation method is employed for converting the semi‐analytical RBTO method to classical RBTO method. To demonstrate the practicability of the proposed framework, three benchmark cases, including 2D and 3D problems, are tested. The results reveal that the proposed framework achieves high accuracy and efficiency.